#### Vol. 5, No. 8, 2011

 Recent Issues
 The Journal Cover Editorial Board Editors' Addresses Editors' Interests About the Journal Scientific Advantages Submission Guidelines Submission Form Subscriptions Editorial Login Contacts Author Index To Appear ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print)
Linear determinantal equations for all projective schemes

### Jessica Sidman and Gregory G. Smith

Vol. 5 (2011), No. 8, 1041–1061
##### Abstract

We prove that every projective embedding of a connected scheme determined by the complete linear series of a sufficiently ample line bundle is defined by the $2×2$ minors of a $1$-generic matrix of linear forms. Extending the work of Eisenbud, Koh and Stillman for integral curves, we also provide effective descriptions for such determinantally presented ample line bundles on products of projective spaces, Gorenstein toric varieties, and smooth varieties.

##### Keywords
determinantally presented, linear free resolution, Castelnuovo–Mumford regularity
##### Mathematical Subject Classification 2000
Primary: 14A25
Secondary: 14F05, 13D02